31A 318

1) (+5) + (-8) =-3

2) (-6) + (+3) + (-4) =-7

3) direction and magnitude

1) sin = oppositehypotenuse

cos = adjacenthypotenuse

tan = oppositeadjacent4) H2=62+82

H2=36+64

~ =100H=10

2) direction and magnitude

3) resultant

4) H2=32+112

H2 = 9+121

H2 =130

H = .J13O= 11.40 miles

5) sin 9 = opposite ~ = .3846hypotenuse 13

cos 9 = adjacent g = .9231hypotenuse 13

tan 9 = opposite = ~ = .4167adjacent 12 5) sin 9 = opposite ~ = .9649

hypotenuse 11.4

cos 9 = adjacent = ~ = .2632hypotenuse 11.4

tan 9 = opposite = .!! = 3.6667adjacent 3

6) sin 9 = .38469= 22.60

7) ~=52+102

H2=25+100

H2 = 125

H= J12s =11.18 miles

tan9=!Q=25

9 = 63.40

11 miles, 63.40

6) tan 9 = 3.66679 = 74.7°

7) H2 = 1002 + 102

H2 = 10,000+ 100

H2 =10,100

H = ~lO, 100 = 100.50 miles

tan 9 =..:!Q. =.1100

9°=5.7" 180-5.7=174.3°8) H2=1002+402

H2 =10,000+1,600

H2 = 11,600H = 107.7miles

tan9=~=.4100

9=21.8°

107.7 miles, 21.80

8) (+4) + (+2) = +6 on the X axis(+3) + (+1) = +4 on the Yaxis

~

'29 4

6

(You could have used sin or cosand gotten the same answer, aslong as you set the. ratio up

correctly.)

9) H2=62+42=36+16=52

H=&=7.21

tan 9 = ~ = .66676

9 = 33.70

, I

5) =:31C

1) H2 = 302 + 402

H2 = 900 + 1600 = 2500

H=h500=50

tan 9 = 40 = 1.333330

9 = 53.10

50 miles, 53.1°

.:2) (+8) + (-5) = +3 on the X axis

(+2) + (+3) = +5 on the Y axis

H2 = 32 + 52 = 9 + 25 = 34

H = .J34 = 5.83

tans =i= 1.666

9 = 59.0°

6) m= -5-(-2) _ -3 3-3-1 - -4 ==4

7) 2[:24 + 3..[8 =2~4·6.(-1)+3m=

2·2·i.[6 + 3'2./2 =

4i.[6 + 6./2

8) X2-16X+64=

(X-8)(X-8) = (X-8l3) Y - x2 = 0Y = x2

X2 _~ X3 -29) __ X __ X __

3 - X2 -3 -X--X -X-

X3 -2 X X3_2--x--=--

X X2 -3 X2-3

4)

(f)Q.S.o·::lenco~

10) X2 -2X-7= 0X = 2 ± ~r-4-- -4 .,-(1"-')(--7---)

2(1)

X= 2±.f322

X = 2 ± 4./2 = 1± 2./22

l>.,,:..&~ co~

o

310

1) H2 = 752 + 1252

H2 = 5625 + 15625 = 21250

H = h1250 ~ 145.77 miles

tan e= 125 = 1.666775

e ~59.0°

2) (-4) + (-1) = -5 on the X axis(+2) + (6) = +8 on the Yaxis

H2 = 52 +82 = 25+64

H2 =89H=.J89 ~ 9.43

tana=~=1.6

a = 57.99°

e = 180° - 57.99° = 122.0°

(+5 is used instead of -5 because distanceor length is always positive. There will bemnrp. nn thic in Prp.r.::aIf"llh Ie \

3) X2 + y2 = 16

4) X2!-3+ YY"X+3

5) X2 - y2 = 4

-2

/2

\1

6) m="2

(4)=!(3)+b2

4=1!+b2

b=2!2

1 1y=-x+2-

2 2

7) 2-/12 ~ .[2 _ 2.[6.J1O . .[2 - ,f5

2.[6 ,f5 2J30,f5 X ,f5 = -5-

8) 6XL X - 2 =(3X - 2)(2X + 1)

!-2 1-2X9) ~4 =_X_= 1-2Xx~= 1-2X

_ 4 X 4 4X X

10) 2X2-3X=2

2X2 -3X-2=0

(2X+1)(X-2)=0

X=-! 22'

31E

1) H2=152+302=225+900

H2 =1125

H = ~1125 ~ 33.54 feet

tan e= 30 = 215

e ~ 63.40

33.5411.63.40

2) (-8) + (+2) = -6 on the X axis(+6) + (-3) = +3 on the Yaxis

H2 = 62 + 32 = 36 + 9 = 45

H= J45 ~6.71

tan a = ~ =.56

a~26.6°e = 1800 -26.6°= 153.4°

3) X - Y2 = 0X = Y2

4) JX =YX=y2 .

'I

5) 4X2 + 9Y2 = 364X2 9y2-+-=136 36

X2 y2-+-=19 4

-2

2~3-3

6) d = ~(6 - (_2))2 +(_3_1)2 =

~64+16 =.J80 ~ 8.9

7) ~ + 6.[2 = 4,13 + 6.J1O=J3,f5 35

20,13 + 18.J1O

15

8) 10X2+23X+12=(5X + 4)(2X + 3)

9) 3B-2A3C _ 2C 7CB2

B2A-3 + A-3 =

3A3C 2A3C. -2----+7A3B2C-B B2 -

A3C-+7A3B2CB2

10) X2+X+1=0

X = -1± ~"1--4-("-1):-;(~1)2(1)

-1±H -1±iJ3--=--2 2

o:Q.S-o':Jenco-'o

~m